Builds are a means of acquiring fighters, and there are several kinds. Other ways to receive fighters include through Achievements and other various points or leaderboard rewards.
Pixite is a bronze-colored "ixstone" (or crystal) that typically makes common fighters, although there are chances to get uncommon, rare, and epic fighters as well. Pixite is dropped from fighters in Normal Mode and raid events, as well as given out as various prizes.
Voxite is a silver-colored crystal that creates uncommon and higher rarity fighters. It is a lot rarer than Pixite and typically acquired from Achievements and other rewards. It can be purchased from the Texi exchange.
Doxite is a gold-colored crystal that is only available during Dungeon events, and typically has a smaller pool of fighters it builds from. Fighters are typically related to the current event. Doxite also has about 50% Ikuppi rate. About a day after the end of a dungeon event, any left over Doxite is converted into Pixite.
Tyxite is a red crystal that primarily creates milestone fighters along with some uncommon fighters and fodders. It is given out during Milestone events and typically limited per player (<100 Tyxite each event).
Similiths are orange, humanoid-shaped artifacts that make a copy of the fighter that dropped it. They are only dropped during Dungeon events. About a day after the end of a dungeon event, any left over Similiths are converted into their respective fighters.
There are also special builds that are typically available from Dotcoins. They all guarantee rare and above fighters.
Premium Builds guarantee rares and have a chance of dropping epics. They cost 300 Dotcoins each except during certain promotions. Typically during events there are special promotions that guarantee an epic or add items with the purchase (such as nux bits, duct tape, or Banunu).
Sign & Tribal Builds: Sign and Tribal builds become available during Elemental Dungeon events and Tribal Dungeon events respectively. They typically guarantee a epic related to that day's Sign/Tribal edge if you build 10 fighters.
Tier Builds: Tier builds increase in price with each step, but guarantee an event specific epic (typically a Paragon, a fighter with a 1000% edge during that event) after 7 steps. They also usually grant several bonuses such as Banunus and Nux Bits.
Revival Builds: Revival builds allow you to get fighters that were given as rewards from past events and that are not available from Pixite or Voxite builds. As the best fighters in the game are those typically acquired as event rewards, this is a rare chance to actually maximize the value of the cash you spent.